Finite Group Databasebeta

← #14656890

Subgroups — #14656890

Order 2816.

402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077001C211yesmaximal, characteristic, complemented
2#13069443C211yesmaximal, characteristic
3#13067177C211yesmaximal, characteristic
4#13067175C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66889—21no—
13C2×#66889—21no—
14#10622598—21no—
15#10622586—21no—
16#10622549C2211yescharacteristic
17C42×Dic11C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622268—22no—
20#10622267—22no—
21#10622108—22no—
22#10622089—22no—
23C2×#4339—21no—
24C2×C11×M16—21no—
25C2×C11×C4⋊C4—21no—
26C2×C42×C11C2311yescharacteristic
27#66983—21no—
28#66983—21no—
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—21no—
31C2×Dic11⋊C4—22no—
32C2×C4×Dic11—21no—
33C2×C4×Dic11—21no—
34C2×C4×Dic11D411yescharacteristic
35C2×C4×Dic11D411yescharacteristic
36#66928—21no—
37#66927Q811yescharacteristic
38C4×D44—21no—
39C4×D44—21no—
40#66922Q811yescharacteristic
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C22⋊C8—21no—
45C4×C8×C11—21no—
46C11×#95—21no—
47C11×#95D412yes—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—21no—
51C11⋊#95D412yes—
52C22⋊(C11⋊C8)—21no—
53#66889—42no—
54#66889—42no—
55C4⋊(C11⋊C8)—21no—
56C4×C11⋊C8—21no—
57#10368—111nomaximal, Sylow
58C22×C4×C11—22no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C2×C22⋊D11—41no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—22no—
66#4339—41no—
67#4339—41no—
68#4339—41no—
69#4339—41no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×C4×D11—41no—
74C2×Dic22—21no—
75C11×M16—41no—
76C11×M16—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C42×C11C2×Q811yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—44no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—44no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—42no—
98C4×Dic11—42no—
99C2×C11⋊C8—41no—
100#2864—111no—
101#1962—111no—
102#1517—111no—
103#1517—111no—
104#1286—111no—
105#1286D1111yescharacteristic, complemented
106#1276—111no—
107C23×C11#12011yescharacteristic
108C22×D11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11C22⋊Q811yescharacteristic
115C2×C4×C11C22⋊Q811yescharacteristic
116C2×C4×C11C22⋊Q811yescharacteristic
117C2×C4×C11#12411yescharacteristic
118C2×C4×C11#12411yescharacteristic
119C2×C4×C11#12411yescharacteristic
120C2×C4×C11#13511yescharacteristic
121C2×C4×C11#13511yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C22⋊D11—81no—
125C22⋊D11—81no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—41no—
135C2×Dic11—42no—
136D44—41no—
137D44—41no—
138D44—81no—
139D44—81no—
140C4×D11—81no—
141C4×D11—81no—
142Dic22—41no—
143Dic22—41no—
144C8×C11—81no—
145C8×C11—81no—
146C11⋊C8—81no—
147#532—111no—
148#431—111no—
149#431C2×D1111yescharacteristic
150#423C2×D1111yescharacteristic
151C2×#104—221no—
152C2×#104—221no—
153#389—221no—
154#389—221no—
155#387—222no—
156#387—222no—
157#382—111no—
158#382C2×D1111yescharacteristic
159C43—111no—
160#327—222no—
161#327—222no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11#39311yescharacteristic
165C22×C11#44911yescharacteristic
166C22×C11#44911yescharacteristic
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—82no—
175C4×C11#47811yescharacteristic
176C4×C11#47811yescharacteristic
177C4×C11#48811yescharacteristic
178C4×C11#49011yescharacteristic
179Dic11—42no—
180Dic11—42no—
181Dic11—82no—
182Dic11—81no—
183C2×#41—221no—
184C2×M16—21no—
185C4⋊Q8—111no—
186#127—111no—
187#124—221no—
188#121—221no—
189#121—221no—
190C4×D4—221no—
191C4×D4—221no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—221no—
196C2×C42—111no—
197C2×C42—111no—
198C2×C42—221no—
199C2×C42—221no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—221no—
205#104—442no—
206#104—442no—
207C22⋊C8—21no—
208C22⋊C8—221no—
209C4×C8—21no—
210C4×C8—221no—
211#95—21no—
212#95—112no—
213#95—222no—
214#95—222no—
215#95—221no—
216#95D4412yes—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11#202511yescharacteristic
220C2×C11#203111yescharacteristic
221C2×C11#203111yescharacteristic
222D11—161no—
223#41—441no—
224#41—441no—
225#41—441no—
226#41—441no—
227C2×Q8—221no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4—441no—
232C22×C4—22no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—222no—
236C22×C4—441no—
237C22×C4C2×D4411yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240M16—41no—
241M16—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—441no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—444no—
250C4⋊C4—444no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C42—221no—
256C42—221no—
257C42—221no—
258C42—221no—
259C42—442no—
260C42—442no—
261C42#433911yescharacteristic
262C42#433911yescharacteristic
263C42#434111yescharacteristic
264C42Q8×D1111yescharacteristic
265C11#1036811yescharacteristic, complemented, Sylow
266C23—441no—
267C23#6693511yescharacteristic
268Q8—441no—
269Q8—441no—
270D4—441no—
271D4—441no—
272D4—881no—
273D4—881no—
274D4—881no—
275D4—881no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—222no—
282C2×C4—222no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—881no—
292C2×C4—881no—
293C2×C4#6692811yescharacteristic
294C2×C4#6693811yescharacteristic
295C2×C4#6693811yescharacteristic
296C2×C4#6694911yescharacteristic
297C2×C4#6694911yescharacteristic
298C2×C4#6695011yescharacteristic
299C2×C4#6696411yescharacteristic
300C2×C4#6696711yescharacteristic
301C2×C4#6696911yescharacteristic
302C2×C4#6697211yescharacteristic
303C8—81no—
304C8—81no—
305C8—881no—
306C22—21no—
307C22—21no—
308C22—881no—
309C22—881no—
310C22—881no—
311C22#1062228611yescharacteristic
312C22#1062239411yescharacteristic
313C22#1062242411yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—442no—
320C4—442no—
321C4—882no—
322C4—881no—
323C4#1062237711yescharacteristic
324C4#1062241311yescharacteristic
325C4#1062248411yescharacteristic
326C4#1062250411yescharacteristic
327C2—21no—
328C2—21no—
329C2—1761no—
330C2#1306976111yescharacteristic
331C2#1306978711yescharacteristic
332C2#1306979111yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1286D11
hypocenterC11#10368
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13077001C2semidirect
5. #13066476C2semidirect
6. #13066448C2semidirect
7. C11×#1286C2semidirect
105. #1286D11semidirect
265. C11#10368semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130770012
#130694432
#130671772
#130671752
#130664762
#130664482
C11×#12862
#1036811